Finite Group Databasebeta

← #12022308

Subgroups — #12022308

Order 1280.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
2C2×#65499C211yesmaximal, characteristic
3C2×#65501C211yesmaximal, characteristic
4C2×C4×#683C211yesmaximal, characteristic, complemented
5C2×#64944C211yesmaximal, characteristic, complemented
6#10602340C211yesmaximal, characteristic
7#10602340C211yesmaximal, characteristic
8#10602338C211yesmaximal, characteristic
9#10602338C211yesmaximal, characteristic
10#10602329C211yesmaximal, characteristic, complemented
11#10602329C211yesmaximal, characteristic, complemented
12#10602327C211yesmaximal, characteristic, complemented
13#10600213C211yesmaximal, characteristic, complemented
14#10600203C211yesmaximal, characteristic, complemented
15#10600200C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×C22⋊Dic5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C4×C5×C22⋊C4—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36#65501—24no—
37#65499C418yescomplemented
38C2×#3963C2211yescharacteristic
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C4×#683—24no—
55#64944—24no—
56#13987—51nomaximal, Sylow
57C25×C5C2311yescharacteristic
58C23×C4×C5—22no—
59C23×C4×C5—22no—
60C23×C4×C5—22no—
61C23×C4×C5—22no—
62C23×C4×C5—41no—
63C23×C4×C5—41no—
64C23×C4×C5C2×C414yes—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4—22no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4Q814yes—
85C2×C42×C5—22no—
86C2×C42×C5—22no—
87C2×C42×C5—22no—
88C2×C42×C5—22no—
89C2×C42×C5—41no—
90C2×C42×C5—41no—
91C2×C22⋊Dic5—22no—
92C2×C22⋊Dic5—22no—
93C2×C22⋊Dic5—22no—
94C2×C22⋊Dic5—22no—
95C2×C22⋊Dic5—22no—
96C2×C22⋊Dic5—22no—
97C2×C22⋊Dic5—41no—
98C2×C22⋊Dic5—41no—
99C2×C22⋊Dic5—41no—
100C2×C22⋊Dic5—41no—
101C2×C22⋊Dic5C2×C414yes—
102C2×C22⋊Dic5C2×C414yes—
103C2×C4⋊Dic5—22no—
104C2×C4⋊Dic5—22no—
105C2×C4⋊Dic5—22no—
106C2×C4⋊Dic5—22no—
107C2×C4⋊Dic5—41no—
108C2×C4⋊Dic5—41no—
109C2×#683—22no—
110C2×#683—22no—
111C2×#683—22no—
112C2×#683—22no—
113C2×#683—22no—
114C2×#683—22no—
115C2×#683—22no—
116C2×#683—22no—
117C2×#683—41no—
118C2×#683—41no—
119C2×#683C2×C414yes—
120C2×#683C2×C414yes—
121C2×C4×Dic5—22no—
122C2×C4×Dic5—22no—
123C2×C4×Dic5—22no—
124C2×C4×Dic5—22no—
125C2×C4×Dic5—22no—
126C2×C4×Dic5—41no—
127C5×#95—22no—
128C5×#95D414yes—
129#3963—22no—
130#3963—22no—
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—22no—
135#3963—22no—
136#3963—22no—
137#3963—41no—
138#3963—41no—
139#3963—41no—
140#3963—41no—
141#3963—41no—
142#3963C2×C414yes—
143#3963C2×C414yes—
144#3963D414yes—
145C2×#387—51no—
146C2×#385—51no—
147C2×#380—51no—
148C2×C4×C4⋊C4—51no—
149C2×C4×C22⋊C4D511yescharacteristic
150#1444—51no—
151#1441—51no—
152#1439—51no—
153#1439—51no—
154#1437—51no—
155#1437—51no—
156#1436—51no—
157#1436—51no—
158#1436—51no—
159#1434—51no—
160C24×C5—21no—
161C24×C5—21no—
162C24×C5—21no—
163C24×C5—21no—
164C24×C5—21no—
165C24×C5—21no—
166C24×C5—21no—
167C24×C5—21no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5C22×C412yes—
173C24×C5C2×Q812yes—
174C24×C5#4112yes—
175C24×C5C2411yescharacteristic
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—28no—
207C22×C4×C5—28no—
208C22×C4×C5—44no—
209C22×C4×C5—44no—
210C22×C4×C5—44no—
211C22×C4×C5—44no—
212C22×C4×C5—44no—
213C22×C4×C5C22×C412yes—
214C22×C4×C5C22×C412yes—
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2×D412yes—
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2×Q812yes—
220C22×C4×C5C2×Q812yes—
221C22×C4×C5#4112yes—
222C22×C4×C5#4112yes—
223C22×C4×C5#4112yes—
224C22×C4×C5#4112yes—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—21no—
256C22×Dic5—21no—
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—21no—
265C22×Dic5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C22×Dic5—21no—
273C22×Dic5C22×C412yes—
274C22×Dic5C22×C412yes—
275C22×Dic5C22×C412yes—
276C22×Dic5C22×C412yes—
277C22×Dic5C2×D412yes—
278C22×Dic5C2×D412yes—
279C22×Dic5#4112yes—
280C22×Dic5#4112yes—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C42×C5—44no—
284C42×C5—44no—
285C22⋊Dic5—28no—
286C22⋊Dic5—44no—
287C22⋊Dic5—44no—
288C22⋊Dic5—44no—
289C4⋊Dic5—44no—
290C4⋊Dic5—44no—
291#683—28no—
292#683—28no—
293#683—28no—
294#683—44no—
295C4×Dic5—28no—
296C4×Dic5—44no—
297C24×C4C2×D511yescharacteristic
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4C2×D511yescharacteristic
309C22×C22⋊C4C2×D511yescharacteristic
310C22×C42—51no—
311C22×C42—51no—
312C22×C42C2×D511yescharacteristic
313C22×C42C2×D511yescharacteristic
314#387—104no—
315#385—58no—
316#380—104no—
317C4×C4⋊C4—104no—
318C4×C22⋊C4—24no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D511yescharacteristic
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—41no—
356C23×C5—41no—
357C23×C5—41no—
358C23×C5—41no—
359C23×C5—41no—
360C23×C5—41no—
361C23×C5—41no—
362C23×C5—41no—
363C23×C5—41no—
364C23×C5—41no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5C4×Q814yes—
372C23×C5C23×C411yescharacteristic
373C23×C5C22×D411yescharacteristic
374C23×C5C22×D411yescharacteristic
375C23×C5C22×Q811yescharacteristic
376C23×C5C2×#4111yescharacteristic
377C23×C5C2×#4111yescharacteristic
378C23×C5C2×#4111yescharacteristic
379C23×C5C2×#4111yescharacteristic
380C23×C5C2×#4111yescharacteristic
381C23×C5C2×#4111yescharacteristic
382C23×C5C2×#4111yescharacteristic
383C23×C5H(5,𝔽2)11yescharacteristic
384C23×C5H(5,𝔽2)11yescharacteristic
385C23×C5H(5,𝔽2)11yescharacteristic
386C23×C52−1+411yescharacteristic
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—416no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5C4×D414yes—
428C2×C4×C5C4×D414yes—
429C2×C4×C5C22⋊Q814yes—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—41no—
452C2×Dic5—41no—
453C2×Dic5—41no—
454C2×Dic5—41no—
455C2×Dic5—41no—
456C2×Dic5—41no—
457C2×Dic5—41no—
458C2×Dic5—41no—
459C2×Dic5—41no—
460C2×Dic5—41no—
461C2×Dic5—41no—
462C2×Dic5—41no—
463C2×Dic5—41no—
464C2×Dic5—41no—
465C2×Dic5—41no—
466C2×Dic5—41no—
467C2×Dic5—41no—
468C2×Dic5—41no—
469C2×Dic5—41no—
470C2×Dic5—41no—
471C2×Dic5—41no—
472C2×Dic5—41no—
473C2×Dic5—41no—
474C2×Dic5—41no—
475C2×Dic5—41no—
476C2×Dic5—41no—
477C2×Dic5—41no—
478C2×Dic5—41no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5—41no—
483C2×Dic5—41no—
484C2×Dic5—41no—
485C2×Dic5#11714yes—
486C25C22×D511yescharacteristic
487C23×C4—22no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—41no—
492C23×C4—41no—
493C23×C4—51no—
494C23×C4—51no—
495C23×C4—51no—
496C23×C4—51no—
497C23×C4—51no—
498C23×C4—51no—
499C23×C4—51no—
500C23×C4—51no—
501C23×C4C4×D514yes—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C23×C4C22×D511yescharacteristic
507C23×C4C22×D511yescharacteristic
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—102no—
511C2×C4⋊C4—102no—
512C2×C4⋊C4—102no—
513C2×C4⋊C4—102no—
514C2×C4⋊C4—102no—
515C2×C4⋊C4—102no—
516C2×C4⋊C4—102no—
517C2×C4⋊C4—102no—
518C2×C4⋊C4—102no—
519C2×C4⋊C4—102no—
520C2×C4⋊C4—102no—
521C2×C4⋊C4—102no—
522C2×C4⋊C4—201no—
523C2×C4⋊C4—201no—
524C2×C4⋊C4—201no—
525C2×C4⋊C4—201no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—102no—
534C2×C22⋊C4—102no—
535C2×C22⋊C4—102no—
536C2×C22⋊C4—102no—
537C2×C22⋊C4—102no—
538C2×C22⋊C4—102no—
539C2×C22⋊C4—201no—
540C2×C22⋊C4—201no—
541C2×C22⋊C4—201no—
542C2×C22⋊C4—201no—
543C2×C22⋊C4Dic1014yes—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—41no—
549C2×C42—41no—
550C2×C42—102no—
551C2×C42—102no—
552C2×C42—102no—
553C2×C42—102no—
554C2×C42—102no—
555C2×C42—201no—
556#95—22no—
557#95—54no—
558#95—54no—
559#95—54no—
560#95—102no—
561#95—102no—
562#95—102no—
563#95—102no—
564#95—102no—
565#95—102no—
566#95—102no—
567#95—102no—
568#95—201no—
569#95—201no—
570#95—201no—
571#95—201no—
572#95—201no—
573#95C22⋊D514yes—
574C22×C5—24no—
575C22×C5—24no—
576C22×C5—24no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—42no—
582C22×C5—42no—
583C22×C5—42no—
584C22×C5—42no—
585C22×C5—42no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5C2×#11711yescharacteristic
590C22×C5C2×C4×D411yescharacteristic
591C22×C5C2×C4×D411yescharacteristic
592C22×C5C2×C4×Q811yescharacteristic
593C22×C5C4×#4111yescharacteristic
594C22×C5#51811yescharacteristic
595C22×C5#52011yescharacteristic
596C22×C5C2×C22⋊Q811yescharacteristic
597C22×C5#52511yescharacteristic
598C22×C5#52511yescharacteristic
599C22×C5#52511yescharacteristic
600C22×C5#52911yescharacteristic
601C22×C5#52911yescharacteristic
602C22×C5#52911yescharacteristic
603C22×C5#53311yescharacteristic
604C22×C5#53811yescharacteristic
605C22×C5#53911yescharacteristic
606C22×C5#54011yescharacteristic
607C22×C5#54211yescharacteristic
608C22×C5D4211yescharacteristic
609C22×C5#54611yescharacteristic
610C22×C5#54611yescharacteristic
611C22×C5#54611yescharacteristic
612C22×C5#54711yescharacteristic
613C22×C5D4×Q811yescharacteristic
614C22×C5#55011yescharacteristic
615C22×C5#55111yescharacteristic
616C22×C5#55211yescharacteristic
617C22×C5#55311yescharacteristic
618C22×C5#55311yescharacteristic
619C22×C5#55411yescharacteristic
620C22×C5#55411yescharacteristic
621C22×C5#55411yescharacteristic
622C22×C5#55511yescharacteristic
623C22×C5#55611yescharacteristic
624C4×C5—24no—
625C4×C5—24no—
626C4×C5—24no—
627C4×C5—42no—
628C4×C5—42no—
629C4×C5—42no—
630Dic5—24no—
631Dic5—42no—
632Dic5—42no—
633Dic5—42no—
634Dic5—42no—
635Dic5—42no—
636Dic5—81no—
637Dic5—81no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24C2×Dic1012yes—
651C24C2×C4×D512yes—
652C24#70912yes—
653C24C23×D511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—52no—
692C22×C4—52no—
693C22×C4—52no—
694C22×C4—52no—
695C22×C4—52no—
696C22×C4—52no—
697C22×C4—52no—
698C22×C4—52no—
699C22×C4—101no—
700C22×C4—101no—
701C22×C4—101no—
702C22×C4—101no—
703C22×C4—101no—
704C22×C4—101no—
705C22×C4—101no—
706C22×C4—101no—
707C22×C4—101no—
708C22×C4—101no—
709C22×C4—101no—
710C22×C4—101no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4—101no—
714C22×C4—101no—
715C22×C4—101no—
716C22×C4—101no—
717C22×C4—101no—
718C22×C4—101no—
719C22×C4—101no—
720C22×C4—101no—
721C22×C4—101no—
722C22×C4—101no—
723C22×C4—101no—
724C22×C4—101no—
725C22×C4—101no—
726C22×C4—101no—
727C22×C4—101no—
728C22×C4—101no—
729C22×C4—101no—
730C22×C4—101no—
731C22×C4—101no—
732C22×C4—101no—
733C22×C4—101no—
734C22×C4—101no—
735C22×C4—101no—
736C22×C4—101no—
737C22×C4—101no—
738C22×C4—101no—
739C22×C4—101no—
740C22×C4—101no—
741C22×C4—101no—
742C22×C4—101no—
743C22×C4—101no—
744C22×C4—101no—
745C22×C4—101no—
746C22×C4—101no—
747C22×C4C2×Dic1012yes—
748C22×C4C2×Dic1012yes—
749C22×C4C2×C4×D512yes—
750C22×C4C2×C4×D512yes—
751C22×C4#70912yes—
752C22×C4#70912yes—
753C22×C4#70912yes—
754C22×C4D4×D512yes—
755C22×C4#71112yes—
756C22×C4C2×C22⋊D512yes—
757C22×C4C2×C22⋊D512yes—
758C22×C4C2×C22⋊D512yes—
759C4⋊C4—108no—
760C4⋊C4—108no—
761C4⋊C4—108no—
762C4⋊C4—204no—
763C4⋊C4—204no—
764C4⋊C4—204no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—108no—
768C22⋊C4—204no—
769C22⋊C4—204no—
770C22⋊C4—204no—
771C42—44no—
772C42—44no—
773C42—108no—
774C42—204no—
775C2×C5—44no—
776C2×C5#229011yescharacteristic
777C2×C5C4×C22⋊Q811yescharacteristic
778C2×C5#233511yescharacteristic
779C2×C5#234511yescharacteristic
780C2×C5#235411yescharacteristic
781C2×C5#235811yescharacteristic
782C2×C5#236011yescharacteristic
783C2×C5#244911yescharacteristic
784C2×C5#245411yescharacteristic
785C2×C5#245611yescharacteristic
786C2×C5#246511yescharacteristic
787C2×C5#246811yescharacteristic
788C2×C5#247611yescharacteristic
789C2×C5#257411yescharacteristic
790C2×C5#257711yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C4×Dic1014yes—
826C23C22×Dic1011yescharacteristic
827C23C22×C4×D511yescharacteristic
828C23C2×#70911yescharacteristic
829C23C2×#70911yescharacteristic
830C23C2×#70911yescharacteristic
831C23C2×#70911yescharacteristic
832C23C2×D4×D511yescharacteristic
833C23C2×#71111yescharacteristic
834C23#414411yescharacteristic
835C23#414411yescharacteristic
836C23D5×#4111yescharacteristic
837C23D5×#4111yescharacteristic
838C23#414911yescharacteristic
839C23#415011yescharacteristic
840C23C22×C22⋊D511yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—416no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—54no—
882C2×C4—102no—
883C2×C4—102no—
884C2×C4—102no—
885C2×C4—102no—
886C2×C4—102no—
887C2×C4—102no—
888C2×C4—102no—
889C2×C4—102no—
890C2×C4—102no—
891C2×C4—102no—
892C2×C4—102no—
893C2×C4—102no—
894C2×C4—102no—
895C2×C4—102no—
896C2×C4—102no—
897C2×C4—102no—
898C2×C4—102no—
899C2×C4—102no—
900C2×C4—102no—
901C2×C4—102no—
902C2×C4—102no—
903C2×C4—201no—
904C2×C4—201no—
905C2×C4—201no—
906C2×C4—201no—
907C2×C4—201no—
908C2×C4—201no—
909C2×C4—201no—
910C2×C4—201no—
911C2×C4—201no—
912C2×C4—201no—
913C2×C4—201no—
914C2×C4—201no—
915C2×C4—201no—
916C2×C4—201no—
917C2×C4—201no—
918C2×C4—201no—
919C2×C4—201no—
920C2×C4—201no—
921C2×C4—201no—
922C2×C4—201no—
923C2×C4—201no—
924C2×C4—201no—
925C2×C4—201no—
926C2×C4—201no—
927C2×C4—201no—
928C2×C4—201no—
929C2×C4—201no—
930C2×C4—201no—
931C2×C4—201no—
932C2×C4—201no—
933C2×C4—201no—
934C2×C4—201no—
935C2×C4—201no—
936C2×C4—201no—
937C2×C4#402714yes—
938C2×C4#407014yes—
939C2×C4C4×C22⋊D514yes—
940C5#1398711yescharacteristic, complemented, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4×Dic1011yescharacteristic
957C22#6580411yescharacteristic
958C22C4×#70911yescharacteristic
959C22#6581311yescharacteristic
960C22C2×#402711yescharacteristic
961C22#6582011yescharacteristic
962C22#6582411yescharacteristic
963C22#6582911yescharacteristic
964C22D5×#11711yescharacteristic
965C22#6585711yescharacteristic
966C22#6586611yescharacteristic
967C22#6586711yescharacteristic
968C22D4×Dic1011yescharacteristic
969C22#6587311yescharacteristic
970C22#6587311yescharacteristic
971C22#6587411yescharacteristic
972C22#6587411yescharacteristic
973C22#6587511yescharacteristic
974C22#6587711yescharacteristic
975C22#6588111yescharacteristic
976C22#6588111yescharacteristic
977C22#6588411yescharacteristic
978C22#6589111yescharacteristic
979C22#6589111yescharacteristic
980C22#6589411yescharacteristic
981C22#6589511yescharacteristic
982C22#6589611yescharacteristic
983C22#6589811yescharacteristic
984C22C2×#407011yescharacteristic
985C22C2×C4×C22⋊D511yescharacteristic
986C22#6612511yescharacteristic
987C22D4×C22⋊D511yescharacteristic
988C22#6614011yescharacteristic
989C22#6615811yescharacteristic
990C22#6616811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—104no—
998C4—202no—
999C4—202no—
1000C4—202no—
1001C4—202no—
1002C4—202no—
1003C4—401no—
1004C4—401no—
1005C2—44no—
1006C2#1060518211yescharacteristic
1007C2#1060518911yescharacteristic
1008C2#1060519611yescharacteristic
1009C2#1060522911yescharacteristic
1010C2#1060527311yescharacteristic
1011C2#1060527611yescharacteristic
1012C2#1060529311yescharacteristic
1013C2#1060532611yescharacteristic
1014C2C4×#407011yescharacteristic
1015C2#1061383011yescharacteristic
1016C2#1061397211yescharacteristic
1017C2#1061409111yescharacteristic
1018C2#1061409411yescharacteristic
1019C2#1061410211yescharacteristic
1020C2#1061414211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13987
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×C4×#683C2semidirect
5. C2×#64944C2semidirect
10. #10602329C2semidirect
11. #10602329C2semidirect
12. #10602327C2semidirect
13. #10600213C2semidirect
14. #10600203C2semidirect
15. #10600200C2semidirect
37. #65499C4semidirect
940. C5#13987semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×C5×C22⋊C42
C2×#654992
C2×#655012
C2×C4×#6832
C2×#649442
#106023402
#106023382
#106023292
#106023272
#106002132
#106002032
#106002002
#139875